"Al Capony" writes in with a very logical question:
If vigilante justice is illegal, why do the police tolerate superheroes? Why am I the only one they're trying to arrest?
Detective Mark Jamieson of the Seattle PD notably said, "just because he's dressed up in costume, it doesn't mean he's in special consideration or above the law." This is high-minded, but impractical. The cops run into a number of problems trying to restrain supers. Let's run down that list, then see what they did about them.
Jurisdiction: Almost every law enforcement agency (LEA), from the FBI down to the campus cops, has a jurisdiction. This can be national or even international in scope, or it can be at the city or state lines. Outside of their turf, the cops lose their power. But by their nature, supers can easily move from place to place, often undetected, and frequently faster than the cops can move themselves.
One of the legal tools created to work around these problems was the escalation of severity for any crime where powers were used. By this, "powers" meant "abilities which a reasonable observer would recognize as superhuman", though that definition has been challenged in court. By making powered crimes, from murder to jaywalking, a Federal case, local LEAs could get Fed assistance, but more importantly, Fed money. In practice this doesn't work as well as anyone hopes. National law enforcement doesn't have the money or manpower to shut down every supervillain.
Technique: A lot of police technique boils down to "exhaust the suspect" - like the early humans who hunted wild animals on the plain, we'd simply out-run the prey until it was tired, then pounce. But supers have far more stamina, resilience, and physical strength than the average police officer. Perp sweating fails miserably for similar reasons. You can still get to supers psychologically, but you can't just lean on them until their bodies grow tired - you'll fail first.
Education has been available for decades on how super biology works, and the international law enforcement community has traded tips on how to effectively deal with supers, but not every little podunk town has the budget to send its officers to class for this sort of thing, and even larger cities like Atlanta or Minneapolis find themselves choosing between supervillain containment training and a few new squad cars.
Economics: The actual cost to restrain a supervillain can be 10 to 50 times that of any dangerous mundane. Apprehension, processing, and incarceration can take a big chunk out of any department's budget. Corporations like Persona might be selling power-suppressing drugs to bigger prisons, but that still costs somebody money.
Alright, so there's serious problems. Then what do the cops do about it?
Stool pigeons, snitches, ringers, and insiders have been tools of law enforcement since there was such a thing as law enforcement. The cops have never shied away from using outsiders to help them do their job, and superheroes are just the latest incarnation of that phenomenon. If a "civilian" wants to "assist the police" in apprehending a bad guy, the cops are perfectly willing to turn a blind eye to how it happened.
Everyone would strongly prefer that heroes turn "legit", of course. Some people, like Bluescreen, did just that - he gave up his old life and became an official lawman out of a sense of civic duty. For those that are willing to work with the cops, but don't want to wear a badge, ACTION exists to bridge the gap and file the paperwork so a hero's bust doesn't get thrown out in court. Some heroes want to do their own thing but not be tied down at all, though. Some do get chased by the cops, but most don't, because it's far more practical to go after the dangerous lawbreakers than the helpful ones.
So the short answer is that the cops tolerate vigilante heroes because they can't afford not to.
P.S. Pyrepower was squealing at your moniker and wanted to know if you're a My Little Pony fan. Kids these days.